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A line parallel to y-axis, cuts the circ...

A line parallel to y-axis, cuts the circle `x^2+y^2=a^2` and parabola. `y^2=-4a(x-a),a lt 0 ` at points P and Q respectively, in the first quadrant. If the lacus of the middle point of P and Q `y=sqrt(a(a-x))+k/4sqrt(a^2-x^2)`, then value is

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